Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
167 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
42 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Infinite-horizon optimal scheduling for feedback control (2402.08819v2)

Published 13 Feb 2024 in eess.SY and cs.SY

Abstract: Emerging cyber-physical systems impel the development of communication protocols to efficiently utilize resources. This paper investigates the optimal co-design of control and scheduling in networked control systems. The objective is to co-design the control law and the scheduling mechanism that jointly optimize the tradeoff between regulation performance and communication resource consumption in the long run. The concept of the value of information (VoI) is employed to evaluate the importance of data being transmitted. The optimal solution includes a certainty equivalent control law and a stationary scheduling policy based on the VoI function. The closed-loop system under the designed scheduling policy is shown to be stochastically stable. By analyzing the property of the VoI function, we show that the optimal scheduling policy is symmetric and is a monotone function when the system matrix is diagonal. Moreover, by the diagonal system matrix assumption, the optimal scheduling policy is shown to be of threshold type. Then we provide a simplified yet equivalent form of the threshold-based optimal scheduling policy. The threshold value searching region is also given. Finally, the numerical simulation illustrates the theoretical result of the VoI-based scheduling.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (39)
  1. G. C. Walsh and H. Ye, “Scheduling of networked control systems,” IEEE Control System Magazine, vol. 21, no. 1, pp. 57–65, 2001.
  2. T. D. Barfoot, State estimation for robotics. Cambridge University Press, 2017.
  3. A. K. Singh, R. Singh, and B. C. Pal, “Stability analysis of networked control in smart grids,” IEEE Transactions on Smart Grid, vol. 6, no. 1, pp. 381–390, 2014.
  4. S. E. Li, Y. Zheng, K. Li, Y. Wu, J. K. Hedrick, F. Gao, and H. Zhang, “Dynamical modeling and distributed control of connected and automated vehicles: Challenges and opportunities,” IEEE Intelligent Transportation Systems Magazine, vol. 9, no. 3, pp. 46–58, 2017.
  5. J. Lunze and D. Lehmann, “A state-feedback approach to event-based control,” Automatica, vol. 46, no. 1, pp. 211–215, 2010.
  6. X. Wang and M. D. Lemmon, “Event-triggering in distributed networked control systems,” IEEE Transactions on Automatic Control, vol. 56, no. 3, pp. 586–601, 2010.
  7. M. Klügel, M. Mamduhi, O. Ayan, M. Vilgelm, K. H. Johansson, S. Hirche, and W. Kellerer, “Joint cross-layer optimization in real-time networked control systems,” IEEE Transactions on Control of Network Systems, vol. 7, no. 4, pp. 1903–1915, 2020.
  8. C. Ramesh, H. Sandberg, L. Bao, and K. H. Johansson, “On the dual effecr in state-based scheduling of networked control systems,” in Proc. of the 2011 American Control Conference (ACC), pp. 2216–2221, 2011.
  9. A. Molin and S. Hirche, “On the optimality of certainty equivalence for event-triggered control systems,” IEEE Transactions on Automatic Control, vol. 58, pp. 470–475, Feb 2013.
  10. T. Soleymani, J. S. Baras, and S. Hirche, “Value of information in feedback control: Quantification,” IEEE Transactions on Automatic Control, 2021.
  11. A. Molin and S. Hirche, “Suboptimal event-triggered control for networked control systems,” ZAMM - Journal of Applied Mathematics and Mechanics, vol. 94, no. 4, pp. 277–289, 2014.
  12. Athena Scientific; 4th edition, 2005.
  13. O. Hernández-Lerma and J. B. Lasserre, “Average cost optimal policies for markov control processes with borel state space and unbounded costs,” Systems & control letters, vol. 15, no. 4, pp. 349–356, 1990.
  14. R. Montes-de Oca, “The average cost optimality equation for markov control processes on borel spaces,” Systems & control letters, vol. 22, no. 5, pp. 351–357, 1994.
  15. E. Gordienko and O. Hernández-Lerma, “Average cost markov control processes with weighted norms: existence of canonical policies,” Applicationes Mathematicae, vol. 23, no. 2, pp. 199–218, 1995.
  16. Springer Science & Business Media, 2012.
  17. G. M. Lipsa and N. C. Martins, “Remote state estimation with communication costs for first-order lti systems,” IEEE Transactions on Automatic Control, vol. 56, no. 9, pp. 2013–2025, 2011.
  18. M. Rabi, K. H. Johansson, and M. Johansson, “Optimal stopping for event-triggered sensing and actuation,” in 2008 47th IEEE Conference on Decision and Control, pp. 3607–3612, IEEE, 2008.
  19. A. S. Leong, S. Dey, and D. E. Quevedo, “Sensor scheduling in variance based event triggered estimation with packet drops,” IEEE Transactions on Automatic Control, vol. 62, no. 4, pp. 1880–1895, 2016.
  20. A. S. Leong, S. Dey, and D. E. Quevedo, “Transmission scheduling for remote state estimation and control with an energy harvesting sensor,” Automatica, vol. 91, pp. 54–60, 2018.
  21. J. Wu, Y. Yuan, H. Zhang, and L. Shi, “How can online schedules improve communication and estimation tradeoff?,” IEEE Transactions on Signal Processing, vol. 61, no. 7, pp. 1625–1631, 2013.
  22. T. Soleymani, J. S. Baras, S. Hirche, and K. H. Johansson, “Value of information in feedback control: Global optimality,” IEEE Transactions on Automatic Control, 2022.
  23. A. Molin, H. Esen, and K. H. Johansson, “Scheduling networked state estimators based on value of information,” Automatica, vol. 110, 2019.
  24. S. Wang, Q. Liu, P. U. Abara, J. S. Baras, and S. Hirche, “Value of information in networked control systems subject to delay,” arXiv preprint arXiv:2104.03355, 2021.
  25. Y. Xu and J. P. Hespanha, “Optimal communication logics in networked control systems,” in Proc. of the 43rd IEEE Conference on Decision and Control (CDC), pp. 3527–3532, IEEE, 2004.
  26. X. Ren, J. Wu, K. H. Johansson, G. Shi, and L. Shi, “Infinite horizon optimal transmission power control for remote state estimation over fading channels,” IEEE Transactions on Automatic Control, vol. 63, no. 1, pp. 85–100, 2017.
  27. J. Chakravorty and A. Mahajan, “Sufficient conditions for the value function and optimal strategy to be even and quasi-convex,” IEEE Transactions on Automatic Control, vol. 63, no. 11, pp. 3858–3864, 2018.
  28. Y. Xu and J. P. Hespanha, “Estimation under uncontrolled and controlled communications in networked control systems,” in Proc. of the 44th IEEE Conference on Decision and Control (CDC), pp. 842–847, IEEE, 2005.
  29. K. J. Åström, Introduction to stochastic control theory. Courier Corporation, 2012.
  30. T. Soleymani, J. S. Baras, S. Hirche, and K. H. Johansson, “Feedback control over noisy channels: Characterization of a general equilibrium,” IEEE Transactions on Automatic Control, 2021.
  31. A. Molin and S. Hirche, “Structural characterization of optimal event-based controllers for linear stochastic systems,” in 49th IEEE Conference on Decision and Control (CDC), pp. 3227–3233, IEEE, 2010.
  32. O. Hernández-Lerma, C. Piovesan, and W. J. Runggaldier, “Numerical aspects of monotone approximations in convex stochastic control problems,” Annals of Operations Research, vol. 56, no. 1, pp. 135–156, 1995.
  33. M. Sanchis, “A note on ascoli’s theorem,” The Rocky Mountain journal of mathematics, pp. 739–748, 1998.
  34. L. Devroye, “Nonparametric density estimation,” The L_1 View, 1985.
  35. Cup Archive, 1980.
  36. S. P. Meyn and R. L. Tweedie, Markov chains and stochastic stability. Springer Science & Business Media, 2012.
  37. W. W. Hager and L. L. Horowitz, “Convergence and stability properties of the discrete riccati operator equation and the associated optimal control and filtering problems,” SIAM Journal on Control and Optimization, vol. 14, no. 2, pp. 295–312, 1976.
  38. L. Narici and E. Beckenstein, “Topological vector spaces, volume 296 of,” Pure and Applied Mathematics (Boca Raton), 2011.
  39. O. Hernández-Lerma and M. Muñoz de Ozak, “Discrete-time markov control processes with discounted unbounded costs: optimality criteria,” Kybernetika, vol. 28, no. 3, pp. 191–212, 1992.

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now
X Twitter Logo Streamline Icon: https://streamlinehq.com

Tweets